Photon Statistics in Millimeter-Submillimeter Wave Astronomy

When looking up to the sky and trying to detect the photons of far away stars that are still in formation, we can get access to knowledge we never had before. In order to do this, we must make sure we truly understand the nature of how photons behave in accordance to each other and to our detectors.In quantum optics we can see that these photons...

Bayesian Estimation of a Monotone Regression Function: A method described by Neelon and Dunson applied to climate data

The goal of this thesis is to implement and experiment with a Bayesian way of estimating a (smooth) monotone regression function by applying it to climate data. The method we use is proposed by Neelon and Dunson. This method uses a piece-wise linear model for the unknown regression function and enforces the monotonicity constraint by the...

Quantum Markov Semigroups and the Lindblad Master Equation: A generalisation to countably infinite dimensional Hilbert spaces of the Lindblad form for generators commuting with the modular automorphism group

Quantum Markov Semigroups (QMS) describe the evolution of a quantum system by evolving a projection or density operator in time. QMS are generated by a generator obeying the well-known Lindblad equation. However, this is a difficult equation. Therefore, the result that the Lindblad form greatly simplifies in the case of the...

Stochastic Genetics

In this bachelor thesis we use a stochastic model to aspire to explain biodiversity patterns in different ecosystems with selection advantage. The stochastic model we use is an extension of the mean­-field voter model where we include a selection factor. In the model individuals with two different types of alleles in two different ecosystems are...

Model based image reconstruction for low-field hand-held MRI: On imaging using field geometry and sample translations

In this report, the conversion from spin-echo signals, obtained with a low-field hand-held MRI scanner that was designed and built at the Leiden University, to images of the proton density within the sample is considered. This scanner does not make use of switchable gradient coils, but instead relies solely on the natural inhomogeneity of the...

Peer assessment in high school mathematics class: Using peer assessment as formative assessment

Peer assessment (PA) is a process that involves students assessing each other’s work and providing their peers with (elaborated) feedback. This thesis investigates how an elaborated form of formative PA can be implemented in the mathematics class to promote students’ achievement in mathematics. A mixed methods investigation at a third-grade...

Aerosol dynamics in human lungs: Modelling deposition fractions under different respiratory conditions

Knowledge of particle deposition is important in clinical settings or when discussing environmental effects of aerosols on humans.<br/>Particle deposition in the human respiratory tract is determined by breathing patterns and lung morphology, as well as particle properties and deposition mechanisms.<br/>In this study we develop a 1-dimensional...

Dissipation in the Abelian sandpile model: Conditions for criticality

The Abelian sandpile model was first introduced by Bak, Tang and Wiesenfeld in 1987. Since then, a lot of researchers have studied this model and similar models, all related by the concept of self-organized criticality. In this thesis, we study a variant on the classical model where dissipative and anti-dissipative vertices are incorporated in...